Question

For the following data set, 5, 9, 12, 15, 19, 21, 22, 22, 24, 26, 27, 27, 31, 33, 33, 34, 37, 38, 60, 70 a) Find the quartiles Q1 Q2 Q3 b) Find the five number summary c) Find the interquartile range (IQR) IQR = d) Find the lower limit LL = e) Find the upper limit UL = f) Identify the potential outliers (Separate each outlier with a comma. Write NPO if there is no potential outlier) The potential outlier(s) are ROUND ALL ANSWERS TO 2 DECIMAL PLACES.

Answer 1

a)  We have given data in increasing order will be,
5,9,12,15,19,21,22,22,24,26,27,27,31,33,33,34,37,38,60,70
Sample size =n=20

...........observation

= 5.25th observation

5.25 th observation lies between 5th and 6th observation

5th observation = 19

6th observation = 21

Therefore, Q1 = 19 + 0.25 (21-19)

=19.5

..............observation

=10.5 th observation

10.5 th observation lies between 10th and 11th observation

10th observation = 26

11th observation = 27

Q2= 26+0.5(27-26)

=26.5

.........observation

=15.75th observation

15.75 th observation lies between 15th and 16th observation

15th observation = 33

16th observation = 34

Q3 = 33+0.75(34-33)

=33.75

b) Five number summary

Min	Q1	Q2	Q3	Max
5	19.5	26.5	33.75	70

c) Interquartile range = Q3-Q1 = 33.75-19.5 = 14.25

d)Lower limit = Q1 - 1.5 * IQR=19.5-1.5*14.25 =-1.875
e) Upper limit = Q3 + 1.5 * IQR =33.75+1.5*14.25 =55.125

f)  For given values lying outside the range of the lower and upper limit is known as potential outliers.

Potential outliers are 60,70

Non potential outliers are 5, 9, 12, 15, 19, 21, 22, 22, 24, 26, 27, 27, 31, 33, 33, 34, 37, 38